Information theory

Diagram of a general communication system from Claude E. Shannon, A Mathematical Theory of Communication, 1948.

Information theory is a branch of applied mathematics, electrical engineering, and computer science which originated primarily in the work of Claude Shannon and his colleagues in the 1940s. It deals with concepts such as information, entropy, information transmission, data compression, coding, and related topics. Paired with simultaneous developments in cybernetics, and despite the criticism of many, it has been subject to wide-ranging interpretations and applications outside of mathematics and engineering.

This page outlines a bibliographical genealogy of information theory in the United States, France, Soviet Union, and Germany in the 1940s and 1950s, followed by a selected bibliography on its impact across the sciences.

Shannon's information theory (1948)

Harry Nyquist, "Certain Factors Affecting Telegraph Speed", Journal of the AIEE 43:2 (February 1924), pp 124-130; repr. in Bell System Technical Journal, Vol. 3 (April 1924), pp 324-346. Presented at the Midwinter Convention of the AIEE, Philadelphia, February 1924. Shows that a certain bandwidth was necessary in order to send telegraph signals at a definite rate. Considers two fundamental factors for the maximum speed of transmission of 'intelligence' [not information] by telegraph: signal shaping and choice of codes. Used in Shannon 1948.

Harry Nyquist, "Certain Topics in Telegraph Transmission Theory", Transactions of AIEE, Vol. 47 (April 1928), pp 617-644; repr. inProceedings of the IEEE 90:2 (February 2002), pp 280-305. Presented at the Winter Convention of the AIEE in New York in February 1928. Argues for the steady-state system over the method of transients for determining the distortion of telegraph signals. In this and his 1924 paper, Nyquist determines that the number of independent pulses that could be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel; this rule is essentially a dual of what is now known as the Nyquist–Shannon sampling theorem. Used in Shannon 1948.

Ralph V.L. Hartley, "Transmission of Information", Bell System Technical Journal 7:3 (July 1928), pp 535-563. Presented at the International Congress of Telegraphy and Telephony, Lake Como, Italy, September 1927. Uses the word information as a measurable quantity, and opts for logarithmic function as its measure, when the information in a message is given by the logarithm of the number of possible messages: H = n log S, where S is the number of possible symbols, and n the number of symbols in a transmission. Used in Shannon 1948.

Robert M. Fano, The Transmission of Information, Technical Reports No. 65 (17 March 1949) and No. 149 (6 February 1950), Research Laboratory of Electronics, MIT. A similar coding technique like Shannon's, only deducted differently. In 1952 optimised by his student, Huffman (see below).

Wiener's cybernetics (1948)

Norbert Wiener, The Extrapolation, Interpolation, and Smoothing of Stationary Time Series, NDRC Report, MIT, February 1942. Classified (ordered by Warren Weaver, then the head of Section D-2), printed in 300 copies. Nicknamed "Yellow Peril". Published in 1949 (see below). Shannon 1948 mentions it as containing "the first clear-cut formulation of communication theory as a statistical problem, the study of operations on time series. This work, although chiefly concerned with the linear prediction and filtering problem, is an important collateral reference in connection with the present paper" (p 626-7). [7], Commentary.

Norbert Wiener, Cybernetics: or Control and Communication in the Animal and the Machine, Paris: Hermann & Cie, 1948; Cambridge, MA: Technology Press, 1948; New York: John Wiley & Sons, 1948, 194 pp; 2nd ed., MIT Press and Wiley, 1961, 212 pp; 1965, PDF; 1980. Reviews: Dubarle (1948, FR), Littauer (1949), MacColl (1950). In the spring of 1947, Wiener was invited to a congress on harmonic analysis, held in Nancy, France and organized by the bourbakist mathematician, Szolem Mandelbrojt. During this stay in France Wiener received the offer to write a manuscript on the unifying character of this part of applied mathematics, which is found in the study of Brownian motion and in telecommunication engineering. The following summer, back in the United States, Wiener decided to introduce the neologism ‘cybernetics’ into his scientific theory. According to Pierre De Latil, MIT Press tried their best to prevent the publication of the book in France, since Wiener, then professor at MIT, was bound to them by contract. As a representative of Hermann Editions, M. Freymann managed to find a compromise and the French publisher won the rights to the book. Having lived together in Mexico, Freymann and Wiener were friends and it is Freymann who is supposed to have suggested that Wiener write this book. Benoît Mandelbrot and Walter Pitts proofread the manuscript. [8]

Colloques Internationaux du Centre National de la Recherche Scientifique 47 (1953). (French). Proceedings of a congress held in Paris in January 1951. Paul Chauchard: the congress was "the first manifestation in France of the young cybernetics, with the participation of N. Wiener, the father of this science." For this congress, organised by the French scientists Louis Couffignal and Pérès, both of whom had visited the U.S. laboratories, and sponsored by the Rockefeller Foundation, a number of foreigners were invited, including Howard Aiken, Warren McCulloch, Maurice Wilkes, Grey Walter, Donald MacKay and Ross Ashby, along with Wiener who was staying in Paris for a couple of months at the Collège de France. 300 people attended; 38 papers were presented; 14 machines from six different countries were demonstrated. [15]

Benoît Mandelbrot, Contributions à la théorie mathématique des jeux de communications, Institut de Statistiques de l'Université de Paris 2, 1953. (French). Ph.D. dissertation in mathematics making a connection between game theory and information theory. He showed for instance that both thermodynamics and statistical structures of language can be explained as results of minimax games between ‘nature’ and ‘emitter’. He also made the connection between the definitions of information given by the British statistician Ronald A. Fisher in the 1920s, by the physicist Dennis Gabor in 1946 and the already well-known definition proposed by Shannon. Mandelbrot was at MIT from 1952-1954 and later at the IAS in Princeton. [16]

Aleksei Liapunov, Anatolii Kitov, Sergei Sobolev, "Osnovnye cherty kibernetiki" [Основные черты кибернетики; Basic Features of Cybernetics], Voprosy filosofii [Вопросы философии; Problems of Philosophy] 141:4 (August 1955). (Russian). The first Soviet article speaking positively about cybernetics and non-technical applications of information theory, authored by three specialists in military computing—Liapunov, a noted mathematician and the creator of the first Soviet programming language; Kitov, an organizer of the first military computing centers; and Sobolev, the deputy head of the Soviet nuclear weapons program in charge of the mathematical support. They presented cybernetics as a general "doctrine of information", of which Shannon’s theory of communication was but one part. The three authors interpreted the notion of information very broadly, defining it as "all sorts of external data, which can be received and transmitted by a system, as well as the data that can be produced within the system." Under the rubric of "information" fell any environmental influence on living organisms, any knowledge acquired by man in the process of learning, any signals received by a control device via feedback, and any data processed by a computer. [18][19]

Debate in Transactions (1955-56)

L.A. De Rosa, "In Which Fields Do We Graze?", I.R.E. Transactions on Information Theory 1 (December 1955). Editorial by the chairman of the Professional Group on Information Theory: "The expansion of the applications of Information Theory to fields other than radio and wired communications has been so rapid that oftentimes the bounds within which the Professional Group interests lie are questioned. Should an attempt be made to extend our interests to such fields as management, biology, psychology, and linguistic theory, or should the concentration be strictly in the direction of communication by radio or wire?"

Claude E. Shannon, "The Bandwagon", I.R.E. Transactions on Information Theory 2 (1956), p 3. Shannon's call for keeping the information theory "an engineering problem": "Workers in other fields should realize that the basic results of the subject are aimed in a very specific direction, a direction that is not necessarily relevant to such fields as psychology, economics, and other social sciences.. [T]he establishing of such applications is not a trivial matter of translating words to a new domain, but rather the slow tedious process of hypothesis and verification. If, for example, the human being acts in some situations like an ideal decoder, this is an experimental and not a mathematical fact, and as such must be tested under a wide variety of experimental situations."

Norbert Wiener, "What Is Information Theory?", I.R.E. Transactions on Information Theory 3 (June 1956), p 48. A rejection of Shannon's narrowing focus and insistance that "information" remain part of a larger indissociable ensemble including all the sciences: "I am pleading in this editorial that Information Theory...return to the point of view from which it originated: that of the general statistical concept of communication.. What I am urging is a return to the concepts of this theory in its entirety rather than the exaltation of one particular concept of this group, the concept of the measure of information into the single dominant idea of all."

Steve J. Heims, Constructing a Social Science for Postwar America: The Cybernetics Group (1946–1953), MIT Press, 1993. A survey of the Macy conferences and dissemination of information theory outside the natural sciences. Review, [30].

Céline Lafontaine, "The Cybernetic Matrix of 'French Theory'", Theory, Culture & Society 24:5 (2007), pp 27-46. On the influence of cybernetics on the development of French structuralism, post-structuralism and postmodern philosophy after WWII.

In other fields

Donna Haraway, "The High Cost of Information in Post World War II Evolutionary Biology: Ergonomics, Semiotics, and the Sociobiology of Communications Systems", Philosophical Forum 13:2-3 (Winter/Spring 1981-82), pp 244-278.

Donna Haraway, "Signs of Dominance: From a Physiology to a Cybernetics of Primate Society, C.R. Carpenter, 1930-1970", in Studies in History of Biology, Vol. 6, eds. William Coleman and Camille Limoges, Johns Hopkins University Press, 1982, pp 129-219.

Philip Mirowski, "What Were von Neumann and Morgenstern Trying to Accomplish?", in Toward a History of Game Theory, ed. E.R. Weintraub, Duke University Press, 1992, pp. 113-147. Information theory in economics.

Indirectly related prior work

Marian Smoluchowski, "Experimentell nachweisbare, der Ublichen Thermodynamik widersprechende Molekularphenomene", Phys. Zeitshur. 13, 1912. Connecting the problem of Maxwell's Demon with that of Brownian motion, Smoluchowski wrote that in order to violate the second principle of thermodynamics, the Demon had to be "taught" [unterrichtet] regarding the speed of molecules. Wiener mentions him in passing in his Cybernetics (1948) [37].